非自治系统用瞬态响应求周期解稳定度的方法

根据Floquet理论关于线性周期系数系统解的性质及稳定性条件 ,定义了衡量非线性非自治系统周期解受扰后的衰减速率指标—稳定度。从动力系统流的概念出发 ,给出了利用非线性非自治系统稳态周期解受扰后的瞬态响应信息计算周期解稳定度的方法。以不平衡滑动轴承 弹性转子系统为例 ,说明了该方法的有效性。将稳定度等于零作为临界判据 ,该方法不仅解决了工频周期解失稳边界的确定问题 ,而且解决了渐进稳定域的估计和抗冲击扰动裕度的计算问题

A Method Evaluating Stability Degree of Periodic Solution Based on Perturbing Response Data in a Non-autonomous system

Stability degree indicates the decay velocity of periodic solution when perturbation disappears. Defined by the Floqued theory about the property and stability degree of periodic solution based on perturbing response data, the stability degree is introduced by aid of the concept of dynamic systems of flow in the paper. Take an unbalanced flexible rotor on lubricated bearing for example, validity of the method has been proved. The critical value of a system is determined by the condition, i.e. stability degree equals zero. Not only parametric limit value but also the asymptotic stability region and the stability margin resisting initial impulse can be determined by this method.